饱和土体中衬砌隧道在移动荷载下的动力响应

为了研究移动点荷载作用下饱和土体全空间中圆形衬砌隧道的三维动力响应,采用解析方法进行求解.用无限长圆柱壳模拟衬砌,用Biot饱和多孔介质模型模拟土体.引入两类势函数表示土骨架和孔隙水的位移,在不同环向模态下利用修正Bessel方程求解各势函数.结合边界条件,得到频率-波数域内衬砌和土骨架位移、孔隙水压力的解答.对各模态下的解答求和,并进行双重Fourier逆变换得到时间-空间域内的动力响应.通过算例分析荷载速度、土体渗透性等对位移及土体孔压的影响.结果表明：饱和土体中衬砌隧道系统存在临界速度,该速度与土体剪切波波速很接近；位移场和孔压场分布受荷载速度、土体渗透性影响较大；随着土体渗透性增大,土体孔压减小；高速荷载时的位移响应频谱与低速荷载时的差别很大．

Dynamic response of lined tunnel in saturated soil due to moving load

An analytical method was presented to investigate the three-dimensional dynamic response of a lined circular tunnel in a full-space saturated poroelastic soil due to a moving pointload. The lining is modeled as a thin cylindrical shell of infinite length, and the soil is modeled as a saturated poroelastic medium using Biots theory. Two kinds of potentials are introduced to express the displacements of soil skeleton and pore fluid, and the modified Bessel equations are employed to obtain the expressions of the potentials for different values of circumferential modenumber. According to boundary conditions, the analytical solutions of the displacements of lining and soil skeleton and the excess pore fluid pressure are obtained in frequency-wavenumber domain. Finally, the time-space domain solutions of the dynamic responses are obtained by operating double inverse Fourier transformation to the sum of all the modal components. The effects of load speed and soil permeability on displacement and pore pressure responses are investigated through the numerical results. The existence of critical speed of the lined tunnel in saturated poroelastic soil is demonstrated, and the critical speed is quite close to the shear wave velocity of the soil. The displacement field and the pore pressure field are greatly influenced by the load velocity and soil permeability. The pore pressure of soil decreases when the soil permeability gets better. The frequency spectrum of the displacement response due to a high speed load is quite different from those due to a low speed load．